There is one type of device for transporting fluids that has almost been forgotten, or overlooked for practical reasons which employs a physical phenomenon commonly known as “Water Hammer”. The first device of this type was built in 1772 by J. Whitehurst for use in a brewery and is classified as “Hydraulic ram pumps” or just “Ram pumps”.
“Water Hammer” is a phenomenon that occurs when a fluid flowing in a pipeline experience a sudden halt by e.g. closing a valve, thereby causing the fluid motion to generate a pressure transients. However, the “Ram pumps” also employ the reversed process, i.e. where pressure transients produces a fluid flow. The reversed process is not part of the “Water Hammer” phenomena, and it has mostly been ignored resulting in a close to non-existing theoretical knowledge about this process. FIG. 1 illustrates a prior art “Ram pump” where a flow of fluid is sent through a “Drive pipe” and a “Waste valve” is employed to generate a positive pressure transient within a “Valve box”. The positive pressure transient is subsequently producing a flow of fluid that transfers at least a fraction of the supplied fluid to the “Storage tank”. The transferred fluid is the same fluid that prior to the transfer was flowing in the “Drive pipe”, and a “Ram pump” is thus a pumping device which utilizes a small fall of fluid to lift a fraction of the supplied fluid to a height that is greater than the initial height of the fluid.
The “Water Hammer” phenomenon also occurs if a body, which is in contact with a fluid at rest, experiences a sufficiently sudden movement, since this is, due to symmetry of relative motion, essentially the same as a sudden halt of a flowing fluid by closing of a valve. An equation relating the pressure transients to the fluid flow speed was formulated by the Russian scientists Nikolai Joukowsky. This equation states that Γ=ρcu, where Γ is the pressure transient, ρ is the density of the fluid, c is the sound speed in the fluid and u is the fluid flow velocity. N. Joukowsky published this equation in 1898 after extensive experiments of the “Water Hammer” phenomena in long steel pipes, and is hence commonly known as the Joukowsky equation. However, the same equation was introduced by the German scientist Johannes von Kries in 1883 based on his studies of blood flow in the arteries.
In industrial pumping application mostly three kinds of pressures are observed: static pressure, pressure waves and pressure transients.
Static pressure is employed in all fluid transporting devices today with only one exception, namely applications where “Ram pumps” are used. Fluids are transported by the gradient of static pressure along the pipelines which the pumping device has established in the system. The static pressure is constant in time during the normal steady state operation of the pumping device, but the pressure is time dependent during the start up of the pump until a steady state is reached. Hence, in the initial phase a pumping device can produce pressure waves. A purely static pressure is not possible to obtain in any industrial pumping application since there will always be some disturbances in the steady state operation. However, various means are applied in order to maintain a close to static situation.
A pressure wave is not capable of generating a net transport of fluids since pressure waves only generate oscillations in a fluid but no net transport. An example of pressure waves are sound waves in air. Notice that the disturbances mention above are mostly pressure waves, and hence one employ different procedures to minimize the generation of these useless pressure waves.
If a pumping device makes a sudden stop due to some failure of the operation of the pump, a pressure transient can be generated in the same way as in the case of a sudden closing of a valve.
In many industrial applications “Water Hammer” is regarded as a dangerous phenomenon that should be avoided due to the plausible occurrence of disruptive cavitations generated by the pressure transients. The pressure transient Γ, which is positive in the beginning, can change sign to become negative due to interactions with some solid surfaces in the system. If the sum of the local pressure and the pressure transient is less than the vapor pressure, cavities containing vapor are formed. After some time the cavity will collapse (implode), i.e. when the pressure in the neighborhood again rises above the vapor pressure. The cavity walls thus rush towards one another thereby generating hard impulse on the system owing to the low degree of compressibility of liquids. The impulses spreading out from each collapsed cavity is an important, and usually undesirable, feature, often heard as disturbingly loud noises in applications such as water supply systems and hydraulic pumps. Most seriously, the continual collapse of cavities leads rapidly to deterioration and erosion of nearby solid surfaces. To summarize one can state that during the “Water Hammer” phenomena all of the positive pressure transients become negative pressure transients, and all of the negative pressure transients are generating disruptive cavitations. Hence, to actively generate the “Water Hammer” phenomena for industrial applications have not been considered feasible among experts in the field.
Pressure transients are avoided in industrial applications, mainly since they would normally lead to disruptive cavitations in the system as in the case of the “Water Hammer” phenomena. One of many reasons to actively produce pressure transients is that pressure transients can be both positive and negative as mention above, and thus pressure transients in a partly enclosed space with one or more openings can produce a flow in the direction out of and into the partly enclosed space. This effect is apparent from the Joukowsky equation Γ=ρcu, thus when Γ is positive u is positive (flow in the direction out of a partly enclosed space), and when Γ is negative u is negative (flow in the direction into a partly enclosed space). In this way both positive and negative pressure transients generate flows, thereby suppressing disruptive cavitations due to negative pressure transients. Notice that only one fraction of the positive pressure transients produces a flow, whereas the other fraction become negative pressure transients due to the abovementioned interactions at some solid surfaces in the system. Since the pressure transients cannot be simultaneously negative and positive, such inflows and outflows may in principle occur through the same opening. The possibility of applying only one opening is an important uniqueness of the described apparatus compared with all fluid transporting devices today that employs one opening for the inflow and one for the outflow. The only exception is the “Ram pump” that has one more opening for the “Waste valve”, thus a “Ram pump” has three openings.
How does the “Ram pump” avoid the disruptive cavitations that normally occur during the “Water Hammer” phenomena? Looking at FIG. 1 one realizes that the “Drive pipe” and the “Supply head” ensures that any disruptive cavitations which are about to develop within the “Valve box” are terminated by a sufficient inflow of fluid from the “Drive pipe”. Hence the sum of the local pressure and the pressure transients are not allowed to become less than the vapor pressure due to this inflow. In other words, any negative pressure transient in the “Valve box” is generating a negative flow (a flow into the “Valve box”) according to the Joukowsky equation. It is important to notice that the hydrostatic head given by the “Supply head” needs to be large enough so that said inflow becomes sufficient to in order to avoid any disruptive cavitations.
What is a pressure transient? There are many ways of generating a static pressure or a pressure wave, but there are only a few known situations where pressure transients occur. The most known case where pressure transients appear is during the “Water Hammer” phenomenon. Pressure transients are a time dependent propagating phenomenon like pressure waves, but unlike pressure waves fluids can be transported by pressure transients in accordance with the Joukowsky equation.
To find out what pressure transients are one need to know more about the concept of pressure in fluids. On a microscopic level pressure is the results of the thermal motion of the particles in the fluid, and one can interpret pressure as energy density in the fluid. However, on a macroscopic level pressure is more commonly regarded as the ability of the fluid to exert a force on a body. The force F that the pressure p inside a hydraulic cylinder can push the piston (body) with is given by F=Ap, where A is the size of the surface of the piston which is in contact with the fluid in the hydraulic cylinder. Hence, a general method of producing a pressure p inside a hydraulic cylinder is to act on the piston (body) with a force F obtaining a pressure given by p=F/A. In this way a static pressure can be generated by a constant force, and a pressure wave is obtained by employing a time dependent oscillating force.
To our knowledge, pressure transients can only be generated by a collision process. The momentum of a fluid flowing in a pipeline (with cross section σ) disappears during a time interval Δt after a valve is suddenly closed, and due to the conservation of momentum something must be created during this time interval Δt. To find out what is happening one can follow the work by N. Joukowsky. Newton second law can be written in the momentum form RΔt=Δ(mu), where F is the force, Δt is a time interval and Δ(mu) is the change in momentum of a body with mass m and velocity u. Applying that a pressure transient can be expressed as Γ=F/σ one can write that ΓσΔt=ρuV=ρuσL=ρuσcΔt, where σ is the cross section of the pipeline, Δt is the time interval during which the momentum ρu disappears, V=σL is the volume V of the part of the fluid (with density ρ) where the momentum has disappeared, and L is the length that the pressure transient Γ has propagated with the sound speed c during the time interval Δt. Hence, the Joukowsky equation Γ=ρcu is obtained.
One could argue that the pressure transient C is generated by a force F as in the case of an ordinary static pressure p, since the relation Γ=F/σ is employed. This is, however, a force that appears in a collision process and the only way to produce such a force is to perform a collision. As mentioned above, pressure transients can be produced by a body (which is in contact with a fluid at rest) which experiences a sufficiently sudden movement. It is now possible to specify more precisely what kind of movement that is needed in order to obtain pressure transients. The movement of said body must be generated by a collision process. The collision process can be obtained with an object (having a nonzero momentum) colliding with said body. More precisely, a collision process is an event where said object is set in motion at time τ and gains a nonzero momentum (during a time interval T) before it collides with said body at a later time τ+T.
The pressure loss p along a pipeline with length L during laminar constant flow is given by the Hagen-Poiseuille equation p=32μLu/d2, where μ is the coefficient of viscosity and u is the fluid flow velocity. Introducing the cross section σ=πd2/4 of the pipeline, the Hagen-Poiseuille equation can be written as p=8πμLu/σ. Hence, an ordinary pumping device must produce a static pressure that is equal to the pressure loss p in order to maintain the fluid flow velocity u in the pipeline. In the case of turbulent flow the pressure loss can be estimated with the Darcy-Weisbach equation p=2fLρu2/d if an empirical friction factor f is introduced, and the dependence of the friction factor f with the Reynolds number is often illustrated in Moody diagrams. It is important to notice that the relation between the flow velocity u and pressure p in both the Hagen-Poiseuille and Darcy-Weisbach equations are different from the relation obtained with the Joukowsky equation Γ=ρcu, hence there is a fundamental difference in how a pressure p and a pressure transient Γ can produce a fluid flow velocity u.
FIG. 8 displays a prior art piston pump where a piston is connected to a machinery, but the mechanical movement of the piston by the machinery is not able to generate pressure transients inside the hydraulic cylinder.
A prior art piston pump is also shown in FIG. 9, but now the piston is moved by a fluid expanding in a chamber. This chamber could be a combustion chamber and the expanding fluid could be some kind of fossil fuel, and again no pressure transients could be produced in the hydraulic cylinder. FIG. 10 outlines a prior art displacement pump where a fluid expanding in the chamber pushes the membrane and thus transport fluid out of the hydraulic cylinder. Such a prior art displacement pump is also disclosed in U.S. Pat. No. 3,586,461. However, the motion of the membrane produces no pressure transients in the hydraulic cylinder.
All the prior arts pumps illustrated in the FIGS. 8-10 and disclosed in U.S. Pat. No. 3,586,461 have one thing in common. They are not able to generated pressure transients, since their operations do not involve any collision process. Hence, the described apparatus therefore employs a heavy object that collides with the piston in order to obtain pressure transients in the hydraulic cylinder.